We introduce the Neural Conditioner (NC), a self-supervised machine able to learn about all the conditional distributions of a random vector X. The NC is a function NC(x⋅a,a,r) that leverages adversarial training to match each conditional distribution P(Xr|Xa=xa). After training, the NC generalizes to sample from conditional distributions never seen, including the joint distribution. The NC is also able to auto-encode examples, providing data representations useful for downstream classification tasks. In sum, the NC integrates different self-supervised tasks (each being the estimation of a conditional distribution) and levels of supervision (partially observed data) seamlessly into a single learning experience.

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement the Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.

We discuss necessary and sufficient conditions for an auto-encoder to define a conservative vector field, in which case it is associated with anenergy function akin to the unnormalized log-probability of the data.We show that the conditions for conservativeness are more general than for encoder and decoder weights to be the same ("tied weights''), and thatthey also depend on the form of the hidden unit activation functions.Moreover, we show that contractive training criteria, such as denoising, enforces these conditions locally.Based on these observations, we show how we can use auto-encoders to extract the conservative component of a vector field.